Electrocatalysis and Catalyst Screening from Density Functional Theory Calculations - Fuel Cell Catalysis: A Surface Science Approach - page 79

and will, in essence, poison the hydrogen evolution process. An expression for the
exchange current density in this regime is derived in [Nørskov et al., 2005]:

1
1 þ exp( DG H = k B T)

i 0 ¼ ek 0 (3 : 24)

where the pre-exponential factor k 0 is the only unknown parameter in the model. As
described above, it has been fitted to experimental data for the exchange current den-
sity for the elemental metals [Nørskov et al., 2005]. For very endothermic adsorption
(DG H . 0), the model predicts that a high barrier for H formation from solvated
protons will lead to low exchange current densities. A rate expression in this regime
is also derived [Nørskov et al., 2005]:

exp( DG H = k B T)
1 þ exp( DG H = k B T)

i 0 ¼ ek 0 (3 : 25)

For (DG H 0), these two regimes are approximately balanced, and a maximum in the
exchange current density is predicted. This is the optimal value of the descriptor, and it
immediately suggests that a reasonable goal for a computational, combinatorial
electrocatalyst search is to find alloys with DG H values close to zero.

3.6.4 Validation of the Model

The model described above is only the first step in a comprehensive description of
HER kinetics. Important extensions would be to consider the effect of alternative
mechanisms (e.g., the Heyrovsky - Volmer mechanism), the detailed effects of chan-
ging hydrogen coverage, and the effects of non-unity transfer coefficients (Brønsted -
Evans - Polanyi coefficients) on the calculated rates. We have, indeed, developed a
substantially more detailed model that incorporates all of these features [Sk ´lason
et al., 2007]. However, while a detailed model of this sort provides significant physical
and chemical insight into the details of the HER, it does not change the fundamental
conclusion that a maximum in activity is found for materials with DG H values of zero.
Hence, the detailed model is, in fact, too detailed to be truly useful for screening of
large numbers of alloys—a simplified model that captures the same activity trends
is more appropriate.
The simplified model does, in fact, do an excellent job of predicting trends in HER
activities and exchange current densities. In Fig. 3.16, we show a comparison of
the model predictions with experimental data for a variety of pure, polycrystalline
metals, for selected single-crystal metals, and for single-crystal Pd overlayers supported
on the close-packed surfaces of a variety of metal substrates [Greeley et al., 2006b].
Clearly, both the theoretical models and the experimental data show rate maxima at
DG H 0, and the quantitative agreement between the experimental and theoretical
rates is reasonable. Given that we are primarily interested in predicting trends in
activities over the various metals and alloys, the model appears to have quite
satisfactory accuracy.